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Riya Manvar
Ans:90

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Ans of Riya Manvar's question, From Nimisha Soni 

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Ans of Riya Manvar's question, From Nimisha Soni 

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Given, CP = DP, CD = 2BC
and P is the midpoint of AB.

AP=AD And PB=BC (opposite side of a parallelogram are equal)

->Now if P is the midpoint of CD and  AB=DC, then DP=PC= 1/2​DC= 1/2​AB..........(eq1)
∠APD=∠DAP ( angles opposite to equal sides are equal)
-> AB∥DC and AP is a transversal,
∠APD=∠PAB ( ALternate interior angles). eq2
From equations 3 and 4, we get

∠DAP=∠PAB= 1/2​∠A
-> CPB=∠PBC (angles opposite to equal sides are equal).
So, AB∥DC and BP are transversal, therefore, ∠CPB=∠PBA.
∠PBC=∠PBA= 1/2∠B

Adjacent sides of a parallelogram are supplementary,∠A+∠B=180 -> 1/2∠A+1/2∠B=90
->In triangle APB,
∠APB+∠PAB+∠PBA=180
∠APB+1/2∠A +1/2∠B=180

∠APB+90=180

∠APB=90, Hence proved the measure is 90 degrees.

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Ans of the Hasti's ques from Nimisha Soni

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Ans of the Hasti's ques from Nimisha Soni

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Ans1.  The volume of hemisphere= 2/3πr^3
=2/3 * 22/7 * (21/100)^3= 0.019404m^3.
(You need to calculate to find the answer here.)

Ans2. Given, the radius of the hemispherical dome is 14.
Find, the required cloth.
C.S.A of hemisphere= 2πr^2
C.S.A= 2* 22/7* (14)^2
C.S.A = 1232 (Calculate n find the ans)
Therefore the required cloth to cover the hemispherical dome is 1232m.

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OC=OB=OA (Radius of circle)
OC=OB
<OCB=<OBC= 54 (Angles opposite to equal sides are equal)
<OCB+<OBC+<BOC=180 (Angle sum property)
57+57+<BOC=180
<BOC=180-114
<BOC=66

OA=OB
<OAB=<OBA=30(Angles opposite to equal sides are equal)
<OAB+<OBA+<AOB=180(Angle sum property)
30+30+<AOB=180
<AOB=180-60
<AOB=120

<AOB=<BOC+<AOC
120=66+<AOC
<AOC=120-66
<AOC=54
Therefore, <AOC=54 and <BOC=66